The meeting also highlighted the potential conflicts of interest inherent in Mr. Trump’s position as both a president and a global real estate developer. Among those at the private session was Jose E. B. Antonio, a developer who is Mr. Trump’s partner on a $150-million, 57-story luxury tower in Manila’s financial district and also serves as Mr. Duterte’s trade envoy to the United States.

The two presidents declined to answer questions during brief remarks to reporters at the start of the meeting. As they sat side by side, Mr. Trump and Mr. Duterte projected a friendly dynamic, ribbing members of the news media as they prepared to speak privately.

“We’ve had a great relationship,” Mr. Trump said, heaping praise on Mr. Duterte’s stewardship of the summit, including an elaborate gala dinner on Sunday where they were seen chatting animatedly and a set of cultural performances on Monday. “This has been very successful.”

Duterte’s Blunt Talk Conjures Society’s Dark Side

With President Trump making a stop in the Philippines, here’s a look at the messages of violence often deployed by the country’s leader, Rodrigo Duterte.

By AINARA TIEFENTHÄLER on Publish Date November 12, 2017.

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“Whoa, whoa — this is not the press statement,” Mr. Duterte said. “We are in a bilateral meeting.”

“You are the spies,” he told the reporters, as Philippine security personnel jostled some of them roughly. The remarks elicited a hearty laugh from Mr. Trump before the journalists were led out of the room.

Mr. Roque later said Mr. Trump focused during the roughly 40-minute session on concerns about tariffs being imposed on American vehicles but not Japanese cars. Mr. Duterte, for his part, thanked the United States for its help in dealing with the conflict in Marawi, the southern city where Philippine forces clashed with militants trying to seize territory.